Approximation (DP IB Applications & Interpretation (AI)): Revision Note

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Approximating Values

How do I know what to round my answer to?

  • Unless otherwise told, always round your answers to 3 significant figures (3 s.f.)

    • Remember: the first significant digit is the first non-zero digit (when reading from left-to-right)

      • Every digit after that is significant

Examiner Tips and Tricks

If an exam question specifies the accuracy required, e.g. 'to 2 decimal places', then you must follow that (and no longer use the 3 significant figure rule).

  • For currency

    • some systems use whole numbers

      • e.g. yen, yuan, peso

    • others use 2 decimal places

      • e.g. dollars, euro, pounds

Are there cases when I have to round up?

  • There are some contexts when it makes sense to round up (or down)

    • e.g. if vehicles hold 5 people each, how many vehicles are needed to take 26 people?

      • 26 over 5 equals 5.2 which rounds to 5

      • However 5 vehicles isn't enough, so round up to 6

Examiner Tips and Tricks

To ensure your final answer is correct to 3 significant figures, your working needs to be to 4 significant figures or more (use exact values where possible).

Worked Example

Let T equals fraction numerator b sin open parentheses 3 a close parentheses over denominator 5 end fraction, where a equals 15 degree and b equals 20.

(a) Calculate the exact value of T.

ai-sl-1-1-3-rounding-we-a

(b) Give your answer from part (a) correct to two decimal places.

ai-sl-1-1-3-rounding-b

(c) Give your answer from part (a) correct to two significant figures.

ai-sl-1-1-3-rounding-c

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